The Problem of Proton Decay - INFN Sezione di...
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 1
The Problem of Proton DecayNeutrino oscillations @Venezia, 8 Feb. 2006
Luciano Maiani Universita’ di Roma “La Sapienza” INFN, Roma, Italy
..an invitation to discuss about the future
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 2
• Standard Model Gauge Group: GSM= SU(3)xSU(2)xU(1): – not simple: 3 couplings, – not even semi-simple: charges not necessarily in rational ratios
BUT in Nature:• charge is quantized: 3Q=integers;• charge MUST be quantized for anomalies to cancel
(Bouchiat, Ilipoulos and Meyer): – anomaly proportional to – For one family: Q(e)+Q(ν)+ 3Q(u)+3Q(d)=-1+3(2/3)-3(1/3) = 0– quarks and leptons must appear in “correlated groups”.
A simple gauge group: why?
A= !doublets Q
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 3
A simple Gauge Group...
• Implies the existence of Super Heavy masses & particles:– g1, g2, g3 → gGUT– couplings run logarithmically, hence it takes a long time to get to
Unification: MGUT ∼1014 -1016 GeV >> MZ (Georgi, Quinn, Weinberg)
• proton decay is induced by new (broken) gauge particle exchange;
• we can relate super heavy MGUT to the remarkable stability of the proton
• experimentally τp >1032-1033 years (see later)
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 4
A family of purely left-handed fields- Replace the field eR with the L-positron field L, (eC)L
- same for the right-handed fields, uR, dRNOTE:
- (eC)L destroys a L-handed positron and creates a R-handed electron;
- [(eC)L ]+ creates a L-handed positron and destryos a R-handed electron, like eR.
- In fact, in the Majorana representation, eC=e+.
- In conclusion: drop the subscript L and write the fields of the first family according to (Q=T3+1/2Y):
€
l =ν
e
Y=−1color=1
;(ec )Y= 2color=1
q =ud
Y=1/ 3color= 3
;(uc )Y=−4 / 3color= 3
;(dc )Y= 2 / 3color= 3
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 5
• SU(5) ⊃SU(3)⊗SU(2)⊗U(1). Use the decomposition:
– T are n2 -1 hermitian, traceless, n x n matrices that generate SU(n), (n=2, 3, 5), – Y=weak hypercharge: Q=T3+1/2Y (Tr Y=0)
– Electric charges are given according to Q=T3+1/2Y. In the fundamental, 5, rep :
•
• “10” the antisymmetric combination of two “5”s.
• 10+5-bar contain all the fields of a family:
€
"5"= (3,0)+2 / 3 + (1,1/2)−1 =
= dc ⊕ l
SU(5) (Georgi & Glashow)
€
TSU (5) =TSU (3) − 2 /3 X
Y TSU (2) +1
€
"5"=
−1/3−1/3−1/3
+10
= (3,0)−2 / 3 + (1,1/2)+1
€
"10"= (3,0)−4 / 3 + (3,1/2)1/ 3 + (1,0)+2
= uc ⊕ q⊕ ec
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 6
• Add an SU(2) singlet, corresponding to a right-handed neutrino:
• SU(2)L singlets can be arranged in doublets of a new weak isospin, SU(2)R:
• The gauge group becomes SU(3)⊗SU(2)L ⊗SU(2)R⊗U(1)Y’ • the old weak hypercharge has been replaced by a new one, Y’, according to:
••• It turns out that:
The left-right symmetric solution: O(10)
€
SU(2)R :
l'c =ec
ν '
Y '= +1color=1
;q'c =dc
uc
Y '=−1/ 3color=1
€
l =ν
e
Y=−1color=1
;(ec )Y= 2color=1
;(ν ')Y= 0color=1
q =ud
Y=1/ 3color= 3
;(uc )Y=−4 / 3color= 3
;(dc )Y= 2 / 3color= 3
€
Q = T3L + T3R +12Y '
€
Y '= B − L
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 7
The Pati - Salam way (bottom-up)• Start from the low energy L-R symmetric group: SU(3)⊗SU(2)L ⊗SU(2)R⊗U(1)Y’ • the two SU(2) gauge couplings are related by Parity, we have 3 gauge couplings as before• A first unification is in the Pati - Salam group, which identifies the lepton number as the 4th color:••••• It is known that:•••• so that we arrive to O(10) (H. Friztsch and P. Minkowski, H. Georgi) along the Pati-Salam way: ••••• The spinorial representation of O(10) is 16 dimensional, and it contains
exactly the fields of one family, 10+5bar + one R-handed neutrino.
€
SU(3)⊗U(1)B−L ⊂ SU(4);ovvero :SU(3)⊗ SU(2)L ⊗ SU(2)R ⊗U(1)B−L ⊂ SU(4)⊗ SU(2)L ⊗ SU(2)R
€
SU(4) =O(6);SU(2)⊗ SU(2) =O(4)
€
SU(3)⊗ SU(2)L ⊗U(1)Y ⊂ SU(3)⊗ SU(2)L ⊗ SU(2)R ⊗U(1)B−L ⊂⊂ SU(4)⊗ SU(2)L ⊗ SU(2) =O(6)⊗O(4)⊂ O(10)
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 8
O(10) and the neutrino mass• The currents of O(10) are in fact vector currents (since they conserve parity): thus O(10) is anomaly-
free.
• O(10) reduces to SU(5) according to: O(10)⊃ U(5)=SU(5)⊗U(1)B-L
• The spinorial rep 16 of O(10) reduces in SU(5) according to:
The formula “explains” the misterious anomaly cancellation between 5-bar and 10
• (ν’)c = νR. A Majorana mass for νR , MR, is SU(5) invariant, and is naturally of order MGUT
• The system νR- νL gives a Majorana neutrino νLwith a very small mass (see-saw):
• for the third generation neutrino: mν ≈ 5 10-2 eV from the oscillations of atmospheric neutrinos, assuming mD=Dirac mass ≈ mtop we find MR ≈ 1015 GeV ≈ MGUT
€
(16)O(10) = (5⊕10⊕1)SU (5)
m!L =m2
D
MR
STRIKINGLY, A SUPERHEAVY MASS APPEARS AGAIN FROM A COMPLETELY INDEPENDENT PHYSICS
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 9
Non-diagonal gauge bosons in SU(5), associated to the generators X and Z =X+, induce baryon number violating transitions :
B-L is conserved
B-violating transitions are also induced by the Triplet component of the Higgs field (a 5):
making H3 superheavy requires very unnatural fine-tuning. A split matter multiplet is also a source of trouble in SUSY GUTs .
Proton Decay in GUTs
€
u→ e+ + X −1/ 3;
€
X −1/ 3 + d→ uc
€
(u + d) + u = p→ (uc + e+) + u = e+ + π 0
H5 =!H3
!
"; H3 =
#
$!1/3!1/3!1/3
%
& ;H2 =!
+10
"
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 10
χ2
Do couplings meet in SU5???Extrapolation to very high energy of the ST running couplings with the couplings determined at LEP (100 GeV) and three families;
MGUT = 1016.1±0.3
GeV
MSUSY = 102.5±1.0
GeV
MSSM
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 11
SUSY introduces new elements in proton decay
• The amplitudes mediated by GUT bosons (dimension 6 operators) become very small
• there is a risk of “weak-like” proton decay (dimension 4 operators), but it can be exorcised with appropriate symmetries (R-symmetry)
• processes mediated by the triplet higgsino emerge (dimension 5 operators)
Proton Decay via dimension five operators: They result from exchange of the lepto-quarks (SUSY partner of H3) followed by gaugino or higgsino dressing.
Amp! !u!d
MH3
· 1
MSUSY
· "S2#
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 12
• In terms of superfields: OLLLL =ΦΦΦL is antisymmetric in color, hence antisymmetric in flavour, so channel with 2nd generation particles dominate:
••• the smallness of the Yukawa couplings wins the day, the dimension 5 contribution is not dissimilar
from usual GUT estimates, but more uncertain
p! K+!̄ or, K0µ+
10!34 yr!1
Dimopoulos, Raby and Wilczek
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 13
• Assumption: some fields satisfy odd boundary conditions in the extra dimension
• n=0 mode forbidden: seen from 4D these particles have a (large) mass, M≈1/R• applies to H3 as well as to the GUT bosons• a new way to generate symmetry breaking (by the way..this is how O. Klein
gave a mass to the W!)• of course non-renormalizable: makes sense only if SUSY GUT is a part of a
consistent theory including gravity, Superstring and the like• SUSY GUT in 5D can have a lot of freedom (see e.g. S. Raby, SUSY02,
DESY)
Extra Dimensions @ GUT scale?
and suppress or enhance proton decay...see e.g.
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 14
The Super-Kamiokande CollaborationarXiv:hep-ex/0502026 v1 15 Feb 2005
NOTE: K+ does not emit Cerenkov light. It is searched via - gamma signal from excited nucleus- K+→π+π0or µ+ν
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 15
✭ S-K 2005
Text
p → π0+e+
SU(5)
p → K+νSUSY
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 16
Getting above 1034y • Massive water Cerenkov detectors in the megaton range:
Hyper Kamiokande• Liquid Argon detectors in the 100 kton range (evolution of
ICARUS in the “Dewar” concept)
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 17
Discovery potential of Water Cerenkov and Liquid Argon technologies
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 18
Can we ever observe superheavy particles???
• Yes...if they are among the relics of the Big Bang...and long lived!
• In this case, their decay products appear as Ultra High Energy Cosmic Rays, above the GKZ cutoff at about 1020 eV;
• A new installation: the Pierre Auger Observatory in Mendoza (Argentina) started in 2005 the observation of extended air showers from UHECR in the austral hemisphere;
• The PA Observatory is operated by a large international collaboration (many groups from CERN Member States!)
• a second site, in Colorado, was decided last year, to observe the northern sky;
• a few slides for Auger, courtesy of prof. Arnulfo Zepeda.
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Montaje del Detector de Superficie
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Sky Map of Data set
Galactic Coordinates
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Auger SD spectrum
29th ICRC Pune
Paul Sommers
Energy scale uncer. still large ~40 % in 100 EeV improvement will come
soon
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 23
Conclusions
• Charge quantization and Anomaly cancellation call for a unified structure for quarks and leptons
• In turn, this requires a SuperHeavy mass level and a finite lifetime for the proton
• The existence of a superheavy mass level is supported by the observed neutrino mass
• Supersymmetry at 1 TeV makes Grand Unification more coherent and calls for p→K+ ν and partial lifetimes in excess of 1033 yrs
• The GUT mass may be the level at which new, Kaluza Klein dimensions show up, solving the Higgs triplet mass puzzle: GUT bosons may be n=1 excited KK particles!
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VENEZIA, 08/02/06 L.MAIANI. Proton Decay 24
Conclusions (cont’d)
• New technologies for water and LAr detectors may allow exploration of the predicted range of lifetimes;
• Decays of superheavy particle may be the source of Ultra High Energy cosmic rays, above the GKZ cutoff at 1020 eV;
• if so, superheavy particles can be studied directly with AUGER and its evolutions like EUSO
• if observed, proton decay offers a wealth of different modes, which should reveal the structure of the B-violating interactions.